Short answer: probably.

Long answer: all life, the simplest example of which is the cell, must be able to locally reduce entropy while increasing the entropy of it's environment. So far that we're aware, this includes metabolic processes, which take simple (comparatively) molecules, restructure and recombine them, and poop out less energetic small molecules. To do this requires big molecular machines, or proteins and enzymes. These big molecules are coded like a computer (in this metaphor, it may be helpful to think of the protein/enzyme as executable code, etc.) by DNA, which again for this metaphor may be thought of as binary. The binary must be translated from 1 & 0 to a programming language, RNA in this case. The RNA may then input executable code. This requires tremendous effort, at least 50 separate proteins (again, coded commands) and only makes binary to code language to executable code. That's one pathway. One fundamental requirement. When you ask about energy metabolism like fermentation, or membrane construction, or things like that, the process gets even more whackadoodle. This is to give you an idea of the complex requirements for the basic concept that life locally reverses entropy. Now consider that for each amino acid of a protein/enzyme (the big machines, the executable code) there are 3 base pairs of DNA called a codon. Each protein can have between 100 and 1 million amino acids. That means that, not counting things like RNA, a genome must be massive for a living thing to actually be alive. Indeed, the smallest confirmed genome of a living thing was isolated from an endosymbiotic organism (a critter that lives in the cell of another critter), Nasuia, that has around 190,000 base pairs of DNA. This thing can only synthesize around 10 amino acids using their DNA. So that's probably the minimal genome possible.